Finite Group Databasebeta

← #50306700

Subgroups — #50306700

Order 38336.

258 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34062762C211yesmaximal, characteristic, complemented
2#34062760C211yesmaximal, characteristic, complemented
3#34062748C211yesmaximal, characteristic, complemented
4#34062744C212yesmaximal, complemented
5#34062739C212yesmaximal, complemented
6#34062735C211yesmaximal, characteristic, complemented
7#34062734C212yesmaximal, complemented
8C2×#23751066C211yesmaximal, characteristic, complemented
9SD16×D599C212yesmaximal, complemented
10#34062723C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C599C211yesmaximal, characteristic, complemented
12#23751078—21no—
13#23751078C2211yescharacteristic
14#23751078C2211yescharacteristic
15#23751077—21no—
16#23751077—22no—
17#23751077C2212yes—
18#23751077C2212yescomplemented
19C2×Dic1198—21no—
20C2×Dic1198C2211yescharacteristic, complemented
21Q8×D599C2212yescomplemented
22C2×C22⋊D599—22no—
23D4×D599—21no—
24D4×D599C2212yes—
25Dic2396C2212yescomplemented
26#23751068C2211yescharacteristic, complemented
27#23751067C2212yescomplemented
28#23751066C2212yescomplemented
29#23751066C2212yescomplemented
30#23751066C2211yescharacteristic, complemented
31#23751065C2211yescharacteristic, complemented
32#23751063C2211yescharacteristic, complemented
33#23751061C2212yescomplemented
34C2×C599⋊C8C2211yescharacteristic, complemented
35C8×D599C2212yescomplemented
36#41×C599C2211yescharacteristic, complemented
37C2×D4×C599C2211yescharacteristic
38SD16×C599C2212yescomplemented
39D8×C599C2212yescomplemented
40M16×C599C2211yescharacteristic, complemented
41C22×D599—22no—
42Dic1198—21no—
43Dic1198—22no—
44Dic1198D411yescharacteristic
45Dic1198C2312yes—
46Dic1198C2311yescharacteristic
47D2396D411yescharacteristic
48D2396C2311yescharacteristic
49C22⋊D599—21no—
50C22⋊D599—22no—
51C22⋊D599—22no—
52C22⋊D599—22no—
53C22⋊D599D412yes—
54C2×Dic599—21no—
55C2×Dic599—22no—
56C2×Dic599—22no—
57C4×D599—22no—
58C4×D599—21no—
59C4×D599C2312yes—
60C599⋊C8C2311yescharacteristic
61C599⋊C8C2311yescharacteristic
62C23×C599—21no—
63Q8×C599C2311yescharacteristic
64D4×C599—21no—
65D4×C599—21no—
66D4×C599C2311yescharacteristic
67D4×C599C2312yes—
68C2×C4×C599—21no—
69C2×C4×C599C2311yescharacteristic
70C8×C599C2312yes—
71C22×C599—21no—
72C22×C599—22no—
73C22×C599—81no—
74C22×C599C2×D411yescharacteristic
75C2×D599—21no—
76C2×D599—82no—
77C2×D599C2×D412yes—
78C4×C599—21no—
79C4×C599C2×D411yescharacteristic
80C4×C599C2411yescharacteristic
81Dic599—21no—
82Dic599—22no—
83Dic599C2×D412yes—
84C2×C599—21no—
85C2×C599—42no—
86C2×C599—41no—
87C2×C599C22×D411yescharacteristic
88D599—22no—
89D599—41no—
90C599#57711yescharacteristic, complemented, Sylow
91#577—5991nomaximal, Sylow
922−1+4—5991no—
93H(5,𝔽2)—5991no—
94#137—5992no—
95#137—5991no—
96AGL(1,ℤ/8)—5992no—
97AGL(1,ℤ/8)D59911yescharacteristic, complemented
98#135—5991no—
99#135—5992no—
100C2×SD16—5991no—
101C2×SD16—5992no—
102#131—5991no—
103#41—5991no—
104#41—5992no—
105#41—5992no—
106#41—5991no—
107#41—11981no—
108#41—11982no—
109#41—11981no—
110#41C2×D59911yescharacteristic, complemented
111C2×Q8—5992no—
112C2×Q8—5991no—
113C2×Q8—11981no—
114C2×D4—5992no—
115C2×D4—11981no—
116C2×D4—11982no—
117C2×D4C2×D59911yescharacteristic
118Q16—5991no—
119Q16—5992no—
120SD16—5991no—
121SD16—5992no—
122SD16—5992no—
123SD16—5991no—
124SD16—5992no—
125SD16C2×D59912yescomplemented
126D8—5991no—
127D8C2×D59912yescomplemented
128M16—5992no—
129M16C2×D59911yescharacteristic, complemented
130C2×C8—5991no—
131C2×C8—5992no—
132C23—21no—
133C23—11982no—
134Q8—5991no—
135Q8—5992no—
136Q8—5991no—
137Q8—11982no—
138Q8—11981no—
139Q8C22×D59911yescharacteristic
140D4—21no—
141D4—21no—
142D4—5992no—
143D4—5991no—
144D4—5991no—
145D4—11982no—
146D4—11982no—
147D4—11982no—
148D4—11981no—
149D4C22×D59911yescharacteristic
150D4C22×D59912yes—
151C2×C4—21no—
152C2×C4—5992no—
153C2×C4—11982no—
154C2×C4—11982no—
155C2×C4—11982no—
156C2×C4—11981no—
157C2×C4—11981no—
158C2×C4C22×D59911yescharacteristic
159C8—5991no—
160C8—5991no—
161C8C22×D59912yes—
162C22—21no—
163C22—22no—
164C22—81no—
165C22—5992no—
166C22—11981no—
167C22—47922no—
168C22D4×D59911yescharacteristic
169C4—21no—
170C4—5992no—
171C4—11981no—
172C4—11982no—
173C4D4×D59911yescharacteristic
174C4C23×D59911yescharacteristic
175C2—21no—
176C2—42no—
177C2—41no—
178C2—23961no—
179C2—11982no—
180C2C2×D4×D59911yescharacteristic
subgroupG/H
centerC2C2×D4×D599
commutator, cosocleC4×C599C24
FrattiniC4C23×D599
FittingAGL(1,ℤ/8)×C599C2
socleC2×C599C22×D4
hypercenterAGL(1,ℤ/8)D599
hypocenterC599#577
LCSG ▷ C4×C599 ▷ C2×C599 ▷ C599
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #34062762C2semidirect
2. #34062760C2semidirect
3. #34062748C2semidirect
4. #34062744C2semidirect
5. #34062739C2semidirect
6. #34062735C2semidirect
7. #34062734C2semidirect
8. C2×#23751066C2semidirect
9. SD16×D599C2semidirect
10. #34062723C2semidirect
11. AGL(1,ℤ/8)×C599C2semidirect
18. #23751077C22semidirect
20. C2×Dic1198C22semidirect
21. Q8×D599C22semidirect
25. Dic2396C22semidirect
26. #23751068C22semidirect
27. #23751067C22semidirect
28. #23751066C22semidirect
29. #23751066C22semidirect
30. #23751066C22semidirect
31. #23751065C22semidirect
32. #23751063C22semidirect
33. #23751061C22semidirect
34. C2×C599⋊C8C22semidirect
35. C8×D599C22semidirect
36. #41×C599C22semidirect
38. SD16×C599C22semidirect
39. D8×C599C22semidirect
40. M16×C599C22semidirect
90. C599#577semidirect
97. AGL(1,ℤ/8)D599semidirect
110. #41C2×D599semidirect
125. SD16C2×D599semidirect
127. D8C2×D599semidirect
129. M16C2×D599semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#340627622
#340627602
#340627482
#340627442
#340627392
#340627352
#340627342
C2×#237510662
SD16×D5992
#340627232
AGL(1,ℤ/8)×C5992
#577599